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counting and probability junior
Problem
The Grunters play the Screamers 4 times. The Grunters are the much better team, and are likely to win any given game. What is the probability that the Grunters will win all 4 games? Express your answer as a common fraction.
Solution
Each of the 4 games is independent of the others, and in each game, the Grunters have probability of winning. Therefore, to get the probability that the Grunters will win all 4 games, we multiply the probabilities that the Grunters win each individual game. This gives:
Final answer
\frac{81}{256}